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To solve the equation \( 5x^{4/3} = 80 \), we can start by isolating \( x^{4/3} \).
1. **Divide both sides by 5**:
\[
x^{4/3} = \frac{80}{5}
\]
\[
x^{4/3} = 16
\]
2. **Now, raise both sides to the power of \( \frac{3}{4} \)** to solve for \( x \):
\[
x = 16^{3/4}
\]
3. **Calculate \( 16^{3/4} \)**:
- First, determine \( 16^{1/4} \):
\[
16^{1/4} = 2 \quad \text{(since \( 16 = 2^4 \))}
\]
- Now raise \( 2 \) to the power of \( 3 \):
\[
16^{3/4} = (16^{1/4})^3 = 2^3 = 8
\]
Thus, the solution to the equation is:
\[
\boxed{8}
\]